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IEEE Trans Pattern Anal Mach Intell ; 39(7): 1309-1319, 2017 07.
Artigo em Inglês | MEDLINE | ID: mdl-27448339


This paper proposes a unified theory for calibrating a wide variety of camera models such as pinhole, fisheye, cata-dioptric, and multi-camera networks. We model any camera as a set of image pixels and their associated camera rays in space. Every pixel measures the light traveling along a (half-) ray in 3-space, associated with that pixel. By this definition, calibration simply refers to the computation of the mapping between pixels and the associated 3D rays. Such a mapping can be computed using images of calibration grids, which are objects with known 3D geometry, taken from unknown positions. This general camera model allows to represent non-central cameras; we also consider two special subclasses, namely central and axial cameras. In a central camera, all rays intersect in a single point, whereas the rays are completely arbitrary in a non-central one. Axial cameras are an intermediate case: the camera rays intersect a single line. In this work, we show the theory for calibrating central, axial and non-central models using calibration grids, which can be either three-dimensional or planar.

IEEE Trans Pattern Anal Mach Intell ; 36(1): 99-112, 2014 Jan.
Artigo em Inglês | MEDLINE | ID: mdl-24231869


We propose a new objective function for clustering. This objective function consists of two components: the entropy rate of a random walk on a graph and a balancing term. The entropy rate favors formation of compact and homogeneous clusters, while the balancing function encourages clusters with similar sizes and penalizes larger clusters that aggressively group samples. We present a novel graph construction for the graph associated with the data and show that this construction induces a matroid--a combinatorial structure that generalizes the concept of linear independence in vector spaces. The clustering result is given by the graph topology that maximizes the objective function under the matroid constraint. By exploiting the submodular and monotonic properties of the objective function, we develop an efficient greedy algorithm. Furthermore, we prove an approximation bound of (1/2) for the optimality of the greedy solution. We validate the proposed algorithm on various benchmarks and show its competitive performances with respect to popular clustering algorithms. We further apply it for the task of superpixel segmentation. Experiments on the Berkeley segmentation data set reveal its superior performances over the state-of-the-art superpixel segmentation algorithms in all the standard evaluation metrics.